Cross Sectional Area For Force Exerted On Plate In Direction Of Flow Of Jet Calculator

Formula Used:

\[ A_{Jet} = \frac{F_{jet} \times [g]}{\gamma_f \times v_{jet}^2 \times (1 + \cos(\theta_t))} \]

Force on Plate in Direction of Jet (F_jet):

Specific Weight of Liquid (γ_f):

kN/m³

Fluid Jet Velocity (v_jet):

m/s

Half of Angle Between Two Tangent to Vane (θ_t):

degrees

Cross Sectional Area of Jet (A_Jet):

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1. What is Cross Sectional Area for Force Exerted on Plate in Direction of Flow of Jet?

The Cross Sectional Area of Jet is the area of a two-dimensional shape that is obtained when a three-dimensional shape is sliced perpendicular to some specified axis at a point. It is calculated based on the force exerted by the jet on a curved vane, specific weight of the liquid, jet velocity, and the angle between tangents to the vane.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A_{Jet} = \frac{F_{jet} \times [g]}{\gamma_f \times v_{jet}^2 \times (1 + \cos(\theta_t))} \]

Where:

\( A_{Jet} \) — Cross Sectional Area of Jet (m²)
\( F_{jet} \) — Force on Plate in Direction of Jet (N)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( \gamma_f \) — Specific Weight of Liquid (kN/m³)
\( v_{jet} \) — Fluid Jet Velocity (m/s)
\( \theta_t \) — Half of Angle Between Two Tangent to Vane (degrees)

Explanation: The formula calculates the cross-sectional area of a jet based on the force it exerts on a curved vane, accounting for fluid properties and geometric configuration.

3. Importance of Cross Sectional Area Calculation

Details: Accurate calculation of jet cross-sectional area is crucial for hydraulic engineering applications, jet propulsion systems, and fluid dynamics analysis where force transfer between fluid and surfaces is involved.

4. Using the Calculator

Tips: Enter force in Newtons, specific weight in kN/m³, velocity in m/s, and angle in degrees (0-90). All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this calculation?
A: This calculation helps determine the effective area through which fluid flows when exerting a specific force on a curved surface, important for designing hydraulic systems and understanding fluid-structure interactions.

Q2: Why is the angle between tangents important?
A: The angle affects how the jet's momentum is transferred to the vane. A smaller angle typically results in more efficient force transfer and different cross-sectional area requirements.

Q3: What are typical values for specific weight of liquids?
A: Water has a specific weight of approximately 9.81 kN/m³, while other liquids vary (e.g., mercury ~133 kN/m³, oil ~8-9 kN/m³).

Q4: How does jet velocity affect the cross-sectional area?
A: Higher jet velocities generally require smaller cross-sectional areas to achieve the same force, as the force is proportional to the square of velocity.

Q5: Are there limitations to this formula?
A: This formula assumes ideal fluid behavior, steady flow conditions, and may not account for factors like fluid viscosity, turbulence, or surface friction in real-world applications.